The present invention relates generally to self-contained breathing systems and more particularly to more effective calculations of remaining air time in systems with high tank pressures.
Various forms of self-contained breathing apparatus form substantially the only means by which human beings are able to safely and effectively function in hostile atmospheric environments. In particular, a self-contained breathing apparatus are essential equipment for divers who wish to remain below the surface for periods of time exceeding their inherent lung capacity, whether for sport, pleasure or to further certain commercial operations such as salvaging, construction and the like. In addition, self-contained breathing apparatus forms essential equipment for service and rescue personnel such as firefighters, paramedics, and the like, that must operate in smoke-filled environments that often include highly toxic gases.
Needless to mention, such self-contained breathing apparatus must include a source of a breathable gas mixture which contains sufficient breathing gas for extended operations in hostile environments. Additionally, such systems must include an apparatus that facilitates delivery of the breathing gas to a user in a safe, effective manner. Pertinent to breathing gas delivery, is the desirability of being able to adequately determine the breathable gas content of a breathing apparatus (or respirator) and be able to express the gas content in terms of the amount of breathing time left available to a user (air time remaining or ATR).
Understanding just how much breathing gas remains in an apparatus and, therefore, how much breathing time this represents, is essential to people who must enter and work in hostile environments. A diver, for example, must understand how much air is remaining in the system in order to allocate sufficient time for a safe decompression program. Likewise, a firefighter must understand how much air time is remaining in order to provide sufficient time to effect a safe exit from a smoke-filled environment or one containing toxic or corrosive gases. Air time remaining is quite possibly the most critical metric with which a user of a self-contained breathing apparatus must be concerned.
Traditionally, self-contained breathing apparatuses can be viewed as falling into two general categories; open circuit and closed or semi-closed circuit. Open circuit systems are typically recognized by the common term SCUBA and represent the most commonly used form of breathing apparatus. Developed and popularized by Jacques Cousteau, open circuit scuba apparatus generally comprises a high pressure tank filled with compressed air, the tank coupled to a demand regulator which supplies the breathing gas to, for example, a diver at the diver""s ambient pressure, thereby allowing the user to breath the gas with relative ease.
However, with open circuit scuba apparatus, even short duration dives at depths greater than 100 feet require a certain amount of decompression time which must be pre-calculated in order to ensure a sufficient volume of breathing gas remains after the dive in order to accommodate decompression. Accordingly, while relatively simple and inexpensive, open circuit scuba apparatus imposes stringent and non-linear constraints on dive time as a consequence of its construction and configuration. This has a direct impact on considerations of air time remaining.
The second form of self-contained breathing apparatus is the closed circuit or semi-closed circuit breathing apparatus, commonly termed a REBREATHER. As the name implies, a rebreather allows a user to xe2x80x9crebreathexe2x80x9d exhaled gas to thus make nearly total use of the oxygen content in its most efficient form. Since only a small portion of the oxygen a person inhales on each breath is actually used by the body, most of this oxygen is exhaled, along with virtually all of the inert gas content, such as nitrogen, and a small amount of carbon dioxide which is generated by the user. Rebreather systems make nearly total use of the oxygen content of the supply gas by removing the generated carbon dioxide and by replenishing the oxygen content of the system to make up for the amount that is consumed by the user.
In all of the above-mentioned cases, whether open circuit or closed or semi-closed circuit, breathing gas is provided in tanks of compressed air, or other gases, of well understood internal volumes, rated to contain breathing gas at particular maximum internal pressures. Indeed, compressed air tanks are often identified in terms of their internal volumetric content, i.e., 10 liter tank, 20 liter tank, and the like, or by an nominal breathing time which a tank would support when filled to its rated capacity, i.e., 30 minute tank, 60 minute tank, and the like.
The amount of breathing gas contained within a given tank can be calculated with reasonable accuracy by simply assuming the ideal gas law;
pV=MRT/mxe2x80x83xe2x80x83(1)
where p is the internal gas pressure in the tank, V is the internal volume of the tank, M is the mass of the breathing gas contained within the tank, R is the universal gas constant (or molar gas constant), T is the temperature of the compressed gas in degrees K, and m is the molecular weight of the gas.
Given the ideal gas assumption above, air time remaining (ATR) can be calculated according to the formula;                               (          ATR          )                =                              p            -                          p              Reserve                                            -                                          ⅆ                p                                            ⅆ                t                                                                        (        2        )            
where pReserve is a chosen reserve pressure and       ⅆ    p        ⅆ    t  
is the instantaneous rate of change of pressure that is a measurement of how quickly gas is being consumed by a user. In practical terms, the instantaneous rate of change of change of pressure can be estimated by xcex94p/xcex94t which is obtained by observing or measuring the change in tank pressure over a relatively short period of time, i.e., approximately 1 minute.
For internal tank pressures in the region of about 2000 psi and below, air time remaining predictions resulting from calculations conducted in accordance with Equations (1) and (2) above are normally sufficiently accurate to allow reasonably safe use. However, modern material science and fabrication techniques have resulted in self-contained breathing apparatus having compressed breathing gas tanks which contain breathing mixtures at pressures of about 4500 psi and even greater. High pressure tank systems such as these are becoming more and more commonplace in both professional and recreational respirator apparatus.
As is well understood by those having skill in the art, the linear ideal gas law, as represented in Equation (1) above, becomes increasingly inaccurate with increasing pressure. Not only does the linear ideal gas law become inaccurate with increasing pressure, but also these inaccuracies can be further perturbed by the molecular make-up of the breathing gas. Each particular gas mixture will have its own particular phase or state response as a function of pressure. Thus, pressure related non-linearities and the ideal gas law for a compressed air mixture will be different than pressure related non-linearities in the case of heliox, for example.
In addition to the deviation of a real gas from the ideal gas law, tank volumes are not always constant. In particular, fire fighters commonly use tanks that are manufactured of wrapped composite materials that, while characterized as generally rigid, still exhibit significant amounts of volumetric expansion at high internal pressures. This volumetric expansion contributes to further non-linearities in air time remaining (ATR) calculations. Finally, pressure transducers contribute an additional source of non-linearities that must be taken into account in ATR calculations.
However caused and to whatever extent exhibited, pressure related non-linearities can lead to considerable inaccuracies in air time remaining predictions when ATR predictions are calculated in accordance with Equations (1) and (2) above. Such inaccuracies in ATR predictions lead to significant safety problems, particularly when a diver""s planned activity schedule and/or decompression profile is calculated on one basis when it actually conforms to another. Firefighters and rescue workers are unable to plan activity in a hostile environment with the strict efficiencies necessary for such high risk activities. Accordingly, there exists a need for self-contained breathing apparatus or respirator systems which operate in conjunction with high breathing gas tank pressures that are able to more effectively and accurately take pressure related non-linearities into account when making air time remaining (ATR) calculations. Such systems should be able to account for different non-linearities exhibited by different breathing gas mixtures.
In a self-contained breathing apparatus of the type including breathing gas contained under pressure in a breathing gas supply tank, a method for accurately determining air time remaining calculates ATR on the basis of a mass of breathing gas contained in the tank by determining a gas supply metric for gas contained in the tank and converting the gas supply metric into a mass. In determining the gas supply metric, the method involves measuring an internal pressure of the tank and solving a non-linear equation which expressly accounts for the non-linearity of a pressure:mass relationship at high pressures. The non-linear equation solution defines a set of ordered pairs of pressure:mass data which are stored in a look-up table.
In particular, the method includes the step of curve fitting a power function to the set of ordered pairs of pressure:mass data, with the function defining a corresponding rate of change of mass from a rate of change of pressure.
In another aspect of the invention, a system for effecting accurate air time remaining determinations in a self-contained breathing apparatus includes sensor means for determining an amount of pressure of a breathing gas within a gas supply tank. Processor means converts measured pressure into a mass equivalent of breathing gas in accordance with a non-linear equation. The processor means thereby determining the air time remaining in the gas supply tank on the basis of an equivalent mass of breathing gas contained in the tank, rather than the measured pressure. A memory is coupled to the processor means in which a set of ordered pairs of pressure:mass data are stored in a look-up table. The ordered pairs of pressure:mass data are produced by solving the non-linear equation, which expressly accounts for the non-linearity of a pressure:mass relationship at high pressures.
The processor means curve fits a power function to the set of ordered pairs of pressure:mass data whereby the function defines a corresponding mass value from a pressure value.